Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

A Pratap,Chuangxia Huang,J Alzabut,R Raja,Jinde Cao

doi:10.1186/s13662-020-02551-x

Abstract

In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

Highlights

Fractional-order differential techniques are employed widely to explore the dynamical behaviors of the networks, especially neural networks (NNs) and complex networks (CNs)
3 Main results we demonstrate the finite-time synchronization and adaptive finite-time synchronization criterion of fractional-order coupled discontinuous neural networks (FCDNNs) (1) and the isolated networks (2) by using graph theory techniques, discontinuous state feedback control, and discontinuous adaptive feedback control
5 Conclusions In this research paper, we have examined the finite-time synchronization and adaptive finite-time synchronization for graph theory perspective FCDNNs

Summary

Introduction

Differential equation and fractional differential equation models have found their applications in a variety of fields including biology [1,2,3,4,5,6], physics [7,8,9,10], engineering [11,12,13,14], mathematics [15,16,17,18], information technology, and so on [19,20,21,22,23,24,25,26,27] They are one of the most rudimentary tools for neural networks. The dynamical behaviors of FONNs have already become a hot research topic, and lots of scientific results have been well published in the literature (see [39,40,41,42,43])

Objectives

Conclusion